This paper investigates infinitely repeated prisoner-dilemma games where the discount factor is less than but close to 1. We assume that players not only imperfectly but also privately monitor their opponents’ choices of action. We provide a likelihood ratio condition under which there exist Nash equilibrium payoff vectors better than the one-shot Nash equilibrium payoff vector. We show that an...

In this paper, we obtain several new generalized KKM-type theorems under a new coercivity condition and the condition of intersectionally closedness which improves condition of transfer closedness. As applications, we obtain new versions of equilibrium problem, minimax inequality, coincidence theorem, fixed point theorem and an existence theorem for an 1-person game.

It is demonstrated that a waveguide consisting of two dielectric slabs may become an all-optical spring when guiding a superposition of two transverse evanescent modes. Both slabs are transversally trapped in stable equilibrium due to the optical forces developed. A condition for stable equilibrium on the wavenumbers of the two modes is expressed analytically. The spring constant characterizing...

(2) NASH EQUILIBRIUM Nash Equilibrium is a solution of a game or a condition in a game involving two or more players, in which no player has anything to gain by changing only his own strategy unilaterally, i.e. no player can benefit by changing his strategy while the other players keep their strategies unchanged. The set of strategy choices and the corresponding payoffs (benefits or rewards) co...

A collocation method with the modified equilibrium on line method (ELM) forimposition of Neumann and Robin boundary conditions is presented for solving the two-dimensionalacoustical problems. In the modified ELM, the governing equations are integrated over the lines onthe Neumann (Robin) boundary instead of the Neumann (Robin) boundary condition equations. Inother words, integration domains are...

Le Chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . However, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. In this article, we derived a simple equation for the violation of...

This paper characterizes the existence of equilibria in minimax inequalities without assuming any form of quasiconcavity of functions and convexity or compactness of choice sets. A new condition, called “local dominatedness property”, is shown to be necessary and further, under some mild continuity condition, sufficient for the existence of equilibrium. We then apply the basic result obtained i...

ABSTRACT. The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under the usual cut-off condition on the collision kernel, we prove a strong stability in L-topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L to eq...

We consider a dynamic version of sender–receiver games, where the sequence of states follows an irreducible Markov chain observed by the sender. Under mild assumptions, we provide a simple characterization of the limit set of equilibrium payoffs, as players become very patient. Under these assumptions, the limit set depends on the Markov chain only through its invariant measure. The (limit) equ...

We consider a two-player partial-information game on a Markov chain, where each player attempts to minimize its own cost over a finite time horizon. We show that this game has always a Nash equilibrium in stochastic behavioral policies. The technique used to prove this result is constructive but has severe limitations because it involves solving an extremely large bi-matrix game. To alleviate t...